You may redact any private information, such as your Internet IP address.

I ask for your routing information, because you just stated that you have a mygate(1) file, containing incorrect information ("192.168.1.1"). Your default route should be assigned by your ISP. If your ISP connection uses DHCP, the default route will be added when you connect. If your ISP connection is static, your ISP should have provided this information.

/etc/mygate is used for static ip address configurations, and describes the default route. Perhaps, if you are using DHCP, a default route is already correctly added, then the use of an incorrect /etc/mygate just causes an error when /etc/netstart issues the route add for it. (That error should appear in /var/log/messages with each boot; you may want to look for it.)
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Run tcpdump against your internal wired network, to see if the incoming Sync packet from the Internet makes it onto the local LAN. Perhaps the source of your problem is the server at 192.168.0.10. If you see packets get sent to the server, but no valid responses, you have a server problem. If you see valid two-way traffic back and forth, then run tcpdump against your external network. On the external network, if you only see the incoming packet, but no outbound responses, you have a routing problem.

Communication between two addresses on the same subnet do not need routing; the underlying subnet protocol (usually Ethernet) provides the addressing (usually MAC), via Address Resolution Protocol (ARP). This is used between your server and your router on the 192.168.0/24 subnet, between your wireless workstations and your router on the 192.168.1/24 subnet, and betwen your router and your ISP's router, on whatever subnet your router connects to within your ISP.

All communications that goes beyond a single subnet must be routed.

A subnet with a single router only needs a default route: the IP address of the router on that subnet. e.g.: Your wireless workstations on 192.168.1/24 need only a default gateway of 192.168.1.1; the address of your OpenBSD router on that subnet. Your wired servers on 192.168.0/24 need only a default gateway of 192.168.0.1; the address of your OpenBSD router on that subnet.

Your OpenBSD router is connected to three different subnets. It's default route should be to your ISPs router somewhere on the em0 subnet.

Change your /etc/pf.conf per the BLUE and RED config fragments. Be careful about OBSERVING the very subtle changes (e.g. no "pass" in the rdr) and differences in keyword spellings (e.g. tag and tagged)